Space of modular forms of level 125, weight 4, and Character 125.g

• Label: 125.4.g
• Level: $125$
• Weight: $4$
• Character orbit: 125.g
• Rep. character: $\chi_{125}(6,\cdot)$
• Character field: $\Q(\zeta_{25})$
• Dimension: $740$
• Newform subspaces: $1$
• Sturm bound: $50$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	125.g (of order \(25\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 125 \)
Character field:			\(\Q(\zeta_{25})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(50\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(125, [\chi])\).

	Total	New	Old
Modular forms	780	780	0
Cusp forms	740	740	0
Eisenstein series	40	40	0

Trace form

\( 740 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 20 q^{6} - 15 q^{7} - 125 q^{8} - 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(125, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
125.4.g.a	$125$	$4$	125.g	125.g	$25$	$740$	$37$	$7.375$		None		$2$	$0$	\(-20\)	\(-20\)	\(0\)	\(-15\)		$\mathrm{SU}(2)[C_{25}]$